reserve x,y,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for PartFunc of C,COMPLEX;
reserve r1,r2,p1 for Real;
reserve r,q,cr1,cr2 for Complex;

theorem
  f|Y is constant implies (for r holds (r(#)f)|Y is bounded) & (-f)|Y is
  bounded & |.f.||Y is bounded
proof
  assume
A1: f|Y is constant;
  hence for r holds (r(#)f)|Y is bounded by Th78,Th80;
  thus (-f)|Y is bounded by A1,Th79,Th80;
  |.f.||Y is constant by A1,Th79;
  hence thesis;
end;
